Pilot Study of Brentuximab Vedotin in Relapsed/Refractory Peripheral T-Cell Lymphoma Expressing CD30

Inclusion Criteria: * Confirmed diagnosis of PTCL expressing CD30 receptor. Following PTCL subtypes will be eligible: Peripheral T - cell lymphoma, not otherwise specified (NOS); Angioimmunoblastic T-cell Lymphoma; Subcutaneous Panniculitis Like T-cell Lymphoma; Hepatosplenic gamma/delta T cell Lymphoma; Extranodal natural killer (NK)T-cell Lymphoma, nasal type; Enteropathy-associated T-cell lymphoma; Adult T-cell Leukemia/lymphoma; T-cell prolymphocytic leukemia; Primary cutaneous gamma-delta T-cell lymphoma; Aggressive NK cell leukemia; Aggressive subtype of T cell Large Granular Lymphocytic (LGL) or transformed LGL leukemia; Epstein Barr Virus(EBV)-positive T-cell lymphoproliferative disorders of childhood; Transformed mycosis fungoides who have progressed following treatment with at least one systemic therapy; Sezary syndrome * Histology slides and pathology material must be available at the site for each patient before enrollment in order to be sent to the Leading Institution of the study for central pathology review and pharmacodynamic studies. * Patients must have progressive, relapsed or refractory disease after: At least one prior systemic anti-lymphoma regimen (chemotherapy or immunotherapy except for transformed mycosis fungoides as described previously); Relapsed or failed autologous or allogeneic stem cell transplant. * Understand and voluntarily sign an Institutional Review Board (IRB) approved informed consent form * Must have at least one site of disease (index lesion) measurable in two dimensions by computed tomography (CT) * Patients with leukemic form of PTCL who will not have a measurable lesion in two dimensions by CT scan, relapsed or refractory disease must be detected by immunohistochemistry or flow cytometry and molecular clonality studies in bone marrow or peripheral blood. * At least 2 weeks since the last chemotherapy, radiation therapy, immunotherapy or any investigational products * Must meet the following criteria within 4 days before the first dose of study drug: * Neutrophils ≥1,000/ul * Hemoglobin ≥ 8 g/dL * Platelets≥ 50.0x10\^9 /L * Total bilirubin ≤ 1.5 x upper normal limit, or ≤ 5 x upper normal limit if documented hepatic involvement with lymphoma or history of Gilbert's Syndrome * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3 x upper normal limit (≤ 5 x upper normal limit if documented hepatic involvement with lymphoma) * Calculated creatinine clearance ≥ 40 mL/min/1.73 m\^2 based on Cockcroft and Gault method * PT or International Normalization Ratio (INR), and Activated Partial Thromboplastin Time (APTT) ≤ 1.5 x upper limit of normal unless patient is receiving anticoagulants. If patient is on anticoagulation therapy, levels should be within therapeutic range. * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Negative pregnancy test for women of childbearing potential * Recovered (≤ Grade 1 toxicity) from the reversible effects of prior antineoplastic therapy Exclusion Criteria: * Any of the following cardiovascular conditions or values within 6 months before the first dose of study drug: Myocardial infarction and the New York Heart Association (NYHA) Class III or IV heart failure * History of another primary malignancy not in clinical remission; except adequately treated patients with completely resected in situ carcinoma, such as nonmelanoma skin cancer and cervical carcinoma in situ on biopsy or a squamous intraepithelial lesion on Pap smear, or localized prostate cancer with prostate-specific antigen (PSA) \<1 ng/ml * Known active cerebral/meningeal involvement with lymphoma. Asymptomatic patients with previously treated and resolved central nervous system (CNS) lymphoma involvement are permitted. * Prior administration of Brentuximab vedotin * Corticosteroid monotherapy for lymphoma within 1 week of the first dose of study drug * Any serious underlying medical condition that, in the opinion of the investigator or medical monitor, would impair the ability to receive or tolerate the planned treatment * Known hypersensitivity to recombinant proteins, or any component contained in the drug formulation * Female patients who are lactating or have a positive serum pregnancy test during the screening period